The aim of this work is to analyze a typical configuration of a Wind Turbine Generator System (WTGS) equipped with a Variable Speed Generator. Nowadays, doublyfed induction generators are being widely used on WTGS, although synchronous generators are being extensively utilized too. There are different types of synchronous generators, but the multi-pole Permanent Magnet Synchronous Generator (PMSG) is chosen in order to obtain its model. It offers better performance due to higher efficiency and less maintenance since it does not have rotor current and can be used without a gearbox, which also implies a reduction of the weight of the nacelle and a reduction of costs. Apart from the generator, the analyzed WTGS consists of another three parts: wind speed, wind turbine and drive train. These elements have been modeled and the equations that explain their behavior have been introduced. What is more, the whole WTGS has been implemented in MATLAB/Simulink interface. Moreover, the concept of the Maximum Power Point Tracking (MPPT) has been presented in terms of the adjustment of the generator rotor speed according to instantaneous wind speed.